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Both leaders spoke for the first time on Friday since Justice Stephen Rares dismissed the lawsuit brought against Mr Slipper by his former staffer James Ashby.

Justice Rares threw out the case on the basis it was an abuse of process and a "political attack" on the former Speaker, finding Mr Ashby had worked in "combination" with Mr Brough in preparing his case.

But speaking to reporters in London Mr Abbott joined other senior Liberal Party figures in defending Mr Brough and confirmed he would remain the LNP's candidate for Fisher.

Mr Abbott's comments came after senior Liberal Arthur Sinodinos said on Thursday night Mr Brough had "questions to answer".

"I think that Mal Brough was perfectly and properly endorsed by the Liberal National Party," Mr Abbott said.

"He's been quite transparent and upfront about his involvement."

It was a suggestion ridiculed by Ms Gillard when she spoke to the ABC a short time later.

She said Mr Abbott had no choice but to strip Mr Brough of his candidacy.

"Mr Brough when he was first asked about this matter lied about it and then was forced to come clean as a result of media inquiries. Mr Brough has been anything but transparent in this matter," Ms Gillard said.

"Mr Abbott needs to require Mr Brough to come here to Parliament House and to stand in front of the Federal Parliamentary Press Gallery and answer every question put to him and then he should still disendorse Mr Brough.

"Mr Brough has been involved in using sexual harassment claims as a political tool. In standing by Mr Brough, Mr Abbott is standing by conduct like that."

Ms Gillard repeated the Labor Party's claim the sexual harassment suit was a "conspiracy" involving a number of senior Coalition figures.

She said the only way the Coalition could remove itself from the "filth they're rolling in" would be for Mr Abbott and others to "come clean" on what they knew.